Finding correlation between U and W

Camila Brandt

Camila Brandt

Answered question

2022-09-23

Two investments X and Y give returns as follows (expectation and variance): E ( X ) = 0.5 , E ( Y ) = 0.4 and V ( X ) = 2 , V ( Y ) = 1 . The correlation between X and Y is ρ ( X ,   Y ) = 0.6 .
Find the expectation and variance of the "combined" investments U = X + Y and W = 2 Y, and finally find the correlation between U and W. Hint: First find V ( U + W ) .

Answer & Explanation

Abram Jacobson

Abram Jacobson

Beginner2022-09-24Added 8 answers

Step 1
First error:
V [ X + Y ] = 2 + 1 + 2 0.6 2 = 3 + 1.2 2
because X, Y are not independent but correlated via ρ = 0.6
Covariance between (U, W), the following definition will help
C o v [ U , W ] = E [ U W ] E [ U ] E [ W ]
substitute U = X + Y and W = 2 Y and find all the expectations w.r.t X, Y
so you can find
E [ U W ] = E [ ( X + Y ) 2 Y ] = 2 E [ X Y ] + 2 E [ Y 2 ]

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Inferential Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?